# Questions tagged [kinetic-theory-of-gases]

Questions about the assumptions, equations, and properties of gases derived from kinetic theory. For questions pertaining to rates of reactions, please use the kinetics tag instead.

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### Calculating the mean free path using the mean square displacement [closed]

I want to obtain the mean free path of a gas by using the mean square displacement, which I have calculated with the formula $$MSD= 2 \cdot D \cdot t$$ where $D$ is the diffusion coefficient of the ...
184 views

### Average molecular distance between hydrogen gas [closed]

The whole question goes like this: Calculate the de Broglie wavelength of hydrogen molecule at 300K (Take the translational energy to be 1.5kT) Compare this to the average intermolecular spacing for ...
73 views

### What is the average collision duration?

So I've been trying to figure this out: What is the average collision duration of a gas in terms of macroscopic variables? What I have figured out. Whenever two molecules collide they must reach a ...
474 views

### Confusion in Van der Waals Equation

I understand that the behavior of ideal gases deviates largely from that of real gases in terms of pressure exerted by the gas molecules on the container in which it is present, space available for ...
36 views

### What ideal gas behavior is observed by a real gas that observes Boyle's law (at Boyle's temperature)?

Boyle's temperature is a constant for a particular gas. At this temperature the real gas behaves ideally. So, does the real gas only follow Boyle's law at this temperature, or are all the gas laws ...
1k views

### Why does gas particle velocity affect rate of effusion?

I understand why smaller particles have more velocity, but I don't understand what velocity has to do with the rate of effusion: My reasoning is thus: Pressure is the number of impacts of particles ...
35 views

### Does KE(avg) stay the same for ideal gas if the PV value changes?

We know that Kinetic Energy is a function of Temperature for an ideal gas. So KE (1 Mole of gas) = (3/2)RT = (3/2)PV. So it's said that even if P or V change their change will counteract the other (...
176 views

### Why do we subtract the volume correction term in the van der Waals gas equation [duplicate]

The following equation is valid for ideal gasses $$pV=nRT$$ Please mind the following notation, any parameter that is related to an ideal gas would be denoted with a subscript $i$ and anything related ...
313 views

### Cubic nature of van der Waals' gas equation

$V_m^3-\dfrac{RT+bP}{P}V_m^2+\dfrac{a}{P}V_m-\dfrac{ab}{P}=0$ So, At $T<T_c$ the above equation has three real roots say $V_1,V_2,V_3$, my doubt is what does this mean physically because for some ...
9k views

### What is the relation between absolute temperature, and rates of diffusion and effusion of a gas?

According to Graham's diffusion law, rate of diffusion is directly proportional to square root of temperature but rate of effusion is inversely proportional to square root of temperature. Why is this ...
1 vote
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1 vote
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### Density gradient vs. entropy of mixing

I was wondering how real gases would behave when they are released into a closed container with fixed volume. For example, suppose we use chlorine and nitrogen gas. Obviously, chlorine has a higher ...
30k views

### Is internal energy equal to (3/2)nRT for an ideal monoatomic gas?

I came across a Khan Academy video providing the following relation for the internal energy of the system $U$: $$U=\frac32nRT,\label{eqn:1}\tag{1}$$ where $n$ is the amount of gas, $R$ is the ...
578 views

### Degrees of freedom of a molecule of N atoms [closed]

Apparently a molecule of N atoms has 3N degrees of freedom. How? Shouldn't it be dependent on the structure of the molecule? How exactly do we derive this?
129 views

### How was it possible to accurately measure the mass of gases in the 19th century?

I have seen periodic tables of Mendeleev (1834-1907) and Newland (1837-1898) in which masses of gases such as oxygen and nitrogen were shown. I don't think there were instruments to measure mass of ...
1k views

### Is air made 100% from atoms?

I know air is made up of roughly 78% nitrogen, 20% oxygen, etc.. but I would like to know what percentage of air is just space and has no atoms at all.
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### Confusion regarding continuity of state

I was reading about Andrew's isotherms and about the continuity of state. What confused me was the continuous conversion of gaseous state to liquid state. Now my textbook says that by keeping volume ...
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1 vote
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### Virial expansion of real gas equation and volume work

Hi I am currently working on a thermodynamics problem, and it asks me to first find the volume work done on a gas that behaves like the simplified Dieterici equation (see below) predicts on isothermal ...
7k views

### Does the Maxwell-Boltzmann distribution apply to gases only?

The Maxwell-Boltzmann distribution can be used to determine the fraction of particles with sufficient energy to react. I know that the curve applies to gaseous reactants and would like to know whether ...
57 views

### Is this a valid interpretation of the Mean relative speed between two (Maxwell-Boltzmann) species?

In textbooks, the collision frequency $Z_{ab}$ is always given as something like: $$Z_{ab} = n_an_b\sigma_{ab} \Bigg(\frac{8 k T}{\pi \mu}\Bigg)^{1/2}= n_an_b\sigma_{ab} \bar{C}_{rel}$$ where the ...
158 views

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### Kinetic energy of molecules in liquid state?

My book (book link) has this question: The kinetic energy of molecules at constant temperature in gaseous state is: more than those in the liquid state less than those in the liquid ...
1 vote
208 views

### Change in pressure?

Consider a sample of gas in a fixed volume container . From the arguments of Kinetic Theory of Gases on quadrupling the temperature what will be the effect on pressure . Basically I thought that the ...
1 vote
839 views

### Does lowering temperature of a gas make it easier to compress?

My teacher said that for ideal gases, the lower the temperature, the lower the kinetic energy of a gas will be, and it will be easier to compress the gas. Using the ideal gas equation $PV=nRT$, if ...
31k views

### Derivation of mean speed from Maxwell–Boltzmann distribution

I found that if a velocity of a gas follows the Maxwell–Boltzmann distribution, the mean velocity is given by $$\langle v \rangle = \sqrt{\frac{8RT}{\pi M}}$$ where $R$ is the gas constant, $T$ is ...
30k views

### Reason for negative Joule Thomson coefficient of Helium and Hydrogen at NTP conditions

Recently, while reading my textbook I came to know that Helium, Hydrogen and Neon are the only gases which have negative Joule Thomson coefficient at NTP conditions, i.e heating effect is observed ...
2k views

### Maximum in Maxwell–Boltzmann distribution [closed]

I need to find the velocity at which the fraction is maximum in Maxwell–Boltzmann distribution $$P(v) = \left(\frac{m}{2\pi kT}\right)^{\frac{3}{2}}4\pi v^2 \exp{\left(-\frac{mv^2}{2kT}\right)}$$ I ...
55 views

### Which formula for kinetic energy of 1 mol of a gas is universally applicable? [duplicate]

I have read 2 formulas for kinetic energy of 1 mol of gas - 3/2 RT and 1/2fRT . But if I equate them then f comes out to be 3 . But f is different of mono, di, polyatomic gases . Where am I wrong in ...
81 views

### Graham's Law of Effusion when Looking at Samples with Equal Mass?

So, I had a question on a chemistry test about two gas samples, one of O2 and one of N2, that had equal masses. We were given the time of effusion for the sample of N2 and then asked to calculate the ...
1 vote
1k views

### Change in Enthalpy in Free Expansion of Ideal and Real gas against Vacuum

By free expansion, I am referring to gas allowed to expand freely against vacuum in a Joule Expansion. If gas is ideal then change in Internal Energy '∆U' and change in Enthalpy '∆H' is zero. (By ∆H = ...
2k views

### Is the average kinetic energy of evaporating water molecules (at room temperature) equivalent to the average kinetic energy of boiling water?

Purpose: On new year's eve, after a splendid red and an assortment of sumptuous repasts, I made a bold remark which, on further consideration, may turn out to be incorrect. Unless! Unless I can ...
923 views

### Why is the speed of ideal gases mass dependent while the kinetic energy is not?

The rms speed of an ideal gas is $v_{\text{rms}}$ = $\sqrt{\frac{3RT}{M} }$ and the kinetic energy is $E_\text{k} = \frac32RT$. From this, it is concluded that the speed is mass dependent, while the ...
130 views

### Question regarding $Z$ (Compressibility factor)

Oh! This problem has been bugging me for a long time. According to Wikipedia, the Compressibility factor $Z$ is defined as the ratio of the volume occupied by a real gas to the volume occupied by an ...
361 views

### Why are some liquids hotter than room temperature gases if liquid and solid molecules move more slowly than gases? [closed]

We learned in school that state change is a matter of molecules moving faster and faster. And we learned "heat em up, speed em up, spread em out". Why then can some liquids have higher ...
So this problem has been bugging me for a long time. According to Wikipedia the compressibility factor $Z$ is defined as the ratio of the volume occupied by a real gas divided by the volume occupied ...